簡約 ln(2*2^{1/5})

解

簡約

ln (2 \cdot 2^{\frac{1}{5}})

\frac{6}{5} ln (2)

十進法表記

0.83177 \dots

解答ステップ

ln (2 \cdot 2^{\frac{1}{5}})

対数の規則を適用する:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (2 \cdot 2^{\frac{1}{5}}) = ln (2) + ln (2^{\frac{1}{5}})

= ln (2) + ln (2^{\frac{1}{5}})

対数の規則を適用する:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (2^{\frac{1}{5}}) = \frac{1}{5} ln (2)

= ln (2) + \frac{1}{5} ln (2)

共通項をくくり出す

ln (2)

= ln (2) (1 + \frac{1}{5})

1 + \frac{1}{5} = \frac{6}{5}

= \frac{6}{5} ln (2)